scholarly journals Three-dimensional quasiperiodic torsional flows in rotating spherical fluids at very low Prandtl numbers

2021 ◽  
Vol 33 (11) ◽  
pp. 114103
Author(s):  
J. Sánchez Umbría ◽  
M. Net
Keyword(s):  
Three Dimensional ◽  
Prandtl Numbers

scholarly journals Bifurcations from steady to quasi-periodic flows in a laterally heated cavity filled with low Prandtl number fluids

2018 ◽  
Vol 861 ◽  
pp. 223-252 ◽  
Author(s):  
A. Medelfef ◽  
D. Henry ◽  
A. Bouabdallah ◽  
S. Kaddeche
Keyword(s):  
Prandtl Number ◽  
Liquid Metals ◽  
Three Dimensional ◽  
Numerical Continuation ◽  
Arnoldi Method ◽  
Periodic Flows ◽  
Bifurcation Points ◽  
Prandtl Numbers ◽  
Stable Flow ◽  
Flow States

This study deals with the transition toward quasi-periodicity of buoyant convection generated by a horizontal temperature gradient in a three-dimensional parallelepipedic cavity with dimensions $4\times 2\times 1$ (length $\times$ width $\times$ height). Numerical continuation techniques, coupled with an Arnoldi method, are used to locate the steady and Hopf bifurcation points as well as the different steady and periodic flow branches emerging from them for Prandtl numbers ranging from 0 to 0.025 (liquid metals). Our results highlight the existence of two steady states along with many periodic cycles, all with different symmetries. The bifurcation scenarios consist of complex paths between these different solutions, giving a succession of stable flow states as the Grashof number is increased, from steady to periodic and quasi-periodic. The change of these scenarios with the Prandtl number, in connection with the crossing of bifurcation points, was carefully analysed.

Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below

1996 ◽  
Vol 326 ◽  
pp. 399-415 ◽  
Author(s):  
M. Wanschura ◽  
H. C. Kuhlmann ◽  
H. J. Rath
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Onset Of Convection ◽  
Buoyant Convection ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
Prandtl Numbers

The stability of steady axisymmetric convection in cylinders heated from below and insulated laterally is investigated numerically using a mixed finite-difference/Chebyshev collocation method to solve the base flow and the linear stability equations. Linear stability boundaries are given for radius to height ratios γ from 0.9 to 1.56 and for Prandtl numbers Pr = 0.02 and Pr = 1. Depending on γ and Pr, the azimuthal wavenumber of the critical mode may be m = 1, 2, 3, or 4. The dependence of the critical Rayleigh number on the aspect ratio and the instability mechanisms are explained by analysing the energy transfer to the critical modes for selected cases. In addition to these results the onset of buoyant convection in liquid bridges with stress-free conditions on the cylindrical surface is considered. For insulating thermal boundary conditions, the onset of convection is never axisymmetric and the critical azimuthal wavenumber increases monotonically with γ. The critical Rayleigh number is less then 1708 for most aspect ratios.

Numerical Study of Three-Dimensional Oscillatory Natural Convection at Low Prandtl Number in Rectangular Enclosures

2000 ◽  
Vol 123 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Shunichi Wakitani
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Width Ratio ◽  
Three Dimensional Flow ◽  
Longitudinal Vortices ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Prandtl Numbers

Numerical investigations are presented for three-dimensional natural convection at low Prandtl numbers (Pr) from 0 to 0.027 in rectangular enclosures with differentially heated vertical walls. Computations are carried out for the enclosures with aspect ratios (length/height) 2 and 4, and width ratios (width/height) ranging from 0.5 to 4.2. Dependence of the onset of oscillation on the Prandtl number, the aspect ratio, and the width ratio is investigated. Furthermore, oscillatory, three-dimensional flow structure is clarified. The structure is characterized by some longitudinal vortices (rolls) as well as cellular pattern.

Solution of Three-Dimensional Transient Heat Transfer During Polymer Injection Molding

2001 ◽  
Author(s):  
Florin Ilinca ◽  
Jean-François Hétu
Keyword(s):  
Heat Transfer ◽  
Injection Molding ◽  
Operator Splitting ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Element Analysis ◽  
Polymer Injection ◽  
Prandtl Numbers ◽  
Polymer Injection Molding

Abstract This paper presents a three-dimensional transient finite element analysis code for solving the flow and heat transfer during polymer injection molding. The problems of interest present important challenges for both the physical modeling and the solution algorithm. The free surface flow of molten polymer moving inside the filling cavity has to be computed as well as the heat transfer between the polymer and the mold. During filling, heat transfer occurs at high Prandtl numbers because of the low material conductivity, resulting in sharp temperature gradients close to the walls. In this work the momentum, energy and front tracking equations are solved in a segregated manner. The energy equation is solved in an operator splitting approach. The methodology is robust and effective in solving three-dimensional industrial parts.

The secondary flow and its stability for natural convection in a tall vertical enclosure

1989 ◽  
Vol 200 ◽  
pp. 189-216 ◽  
Author(s):  
Arnon Chait ◽  
Seppo A. Korpela
Keyword(s):  
Three Dimensional ◽  
Pseudospectral Method ◽  
Base Flow ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Grashof Number ◽  
Practical Applications ◽  
Prandtl Numbers ◽  
Dependent Flow

The multicellular flow between two vertical parallel plates is numerically simulated using a time-splitting pseudospectral method. The steady flow of air, and the time-periodic flow of oil (Prandtl numbers of 0.71 and 1000, respectively) are investigated and descriptions of these flows using both physical and spectral approaches are presented. The details of the time dependency of the flow and temperature fields of oil are shown, and the dynamics of the process is discussed. The spectral transfer of energy among the axial modes comprising the flow is explored. The spectra of kinetic energy and thermal variance for air are found to be smooth and viscously dominated. Similar spectra for oil are bumpier, and the dynamics of the time-dependent flow are determined to be confined to the lower end of the spectrum alone.The three-dimensional linear stability of the multicellular flow of air is parametrically studied. The domain of stable two-dimensional cellular motion was found to be constrained by the Eckhaus instability and by two types of monotone instability. The two-dimensional multicellular flow is unstable above a Grashof number of about 8550 (with the critical Grashof number for the base flow being 8037). Therefore the flow of air in a sufficiently tall vertical enclosure should be considered to be three-dimensional for most practical applications.

Steady three-dimensional convection at high Prandtl numbers

1983 ◽  
Vol 127 (-1) ◽  
pp. 141 ◽  
Author(s):  
H. Frick ◽  
F. H. Busse ◽  
R. M. Clever
Keyword(s):  
Three Dimensional ◽  
Prandtl Numbers

Nonlinear transition in three-dimensional convection

1987 ◽  
Vol 174 ◽  
pp. 357-379 ◽  
Author(s):  
R. Kessler
Keyword(s):  
Spatial Structure ◽  
Three Dimensional ◽  
Theoretical Data ◽  
Boussinesq Equations ◽  
Dynamical Behaviour ◽  
Time Dependent ◽  
Dimensional Structure ◽  
Subharmonic Bifurcation ◽  
Confined Flow ◽  
Prandtl Numbers

Steady and oscillatory convection in a rectangular box heated from below are studied by means of a numerical solution of the three-dimensional, time-dependent Boussinesq equations. The effect of the rigid sidewalls of the box on the spatial structure and the dynamical behaviour of the flow is analysed. Both conducting and adiabatic sidewalls are considered. Calculated streamlines illustrate the three-dimensional structure of the steady flow with Prandtl numbers 0.71 and 7. The onset and the frequency of the oscillatory instability are calculated and compared with available experimental and theoretical data. With increasing Rayleigh number a subharmonic bifurcation and the onset of a quasi-periodic flow can be observed. A comparison of the different time-dependent solutions shows some interesting relations between the spatial structure and the dynamical behaviour of the confined flow.

Natural Convection Within an Elongated Vertical Cylinder: Heat Loss From Bore of Oil Well Christmas Tree

2012 ◽  
Author(s):  
Mauricio A. Sanchez ◽  
Egidio (Ed) Marotta ◽  
Sumit Arora
Keyword(s):  
Oil And Gas ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Vertical Surface ◽  
Density Variation ◽  
Primary Objective ◽  
Christmas Tree ◽  
Oil Well ◽  
Fluid Properties ◽  
Prandtl Numbers

Internal natural convective heat transfer from a thin walled, vertical cylinder with an exposed vertical surface is investigated numerically. The top and bottom end faces are assumed isothermal. This setup approximates the vertical wellbore of a christmas tree for simulating cool-down of subsea oil and gas equipment during shutdown operations. The primary objective of this study is to determine the cooling rate of the interior fluid and the onset of fluid rotation caused by the two non-adiabatic surfaces as a function of Biot (Bi) at the vertical cylindrical wall. The flow is assumed to be three-dimensional, non-steady, and transitional with constant fluid properties except for the density variation with temperature. This latter effect gives rise to the buoyancy forces; being treated by using the Boussinesq approach. The solution is obtained by numerically solving the governing equations; these equations were written in terms of dimensionless variables. The solution is obtained using a commercial finite element method based-code, COMSOL Multiphysics. The specific application that motivated this investigation involved a range of Prandtl numbers (Pr) from 0.7, to 168. The results for these cases are presented herein. In addition, a range of other governing parameters has been considered. From the numerical results for small and moderate values of Rayleigh number, it is observed that steady state solutions (i.e. temperature and velocity) are stratified at the source temperature region regardless of the Biot number.

Numerical Prediction of Fluid Flow and Heat Transfer in a Circular Tube With Longitudinal Fins Interrupted in the Streamwise Direction

1990 ◽  
Vol 112 (2) ◽  
pp. 342-348 ◽  
Author(s):  
K. M. Kelkar ◽  
S. V. Patankar
Keyword(s):  
Heat Transfer ◽  
Axial Velocity ◽  
Three Dimensional ◽  
Axial Direction ◽  
Streamwise Direction ◽  
Initial Development ◽  
Repetitive Nature ◽  
Staggered Arrangement ◽  
Prandtl Numbers ◽  
Parabolic Flow

Numerical calculations have been made for the performance prediction of laminar flow through circular tubes with longitudinal fins interrupted in the streamwise direction by arranging them either in a staggered or an in-line manner. Calculations are made for three-dimensional parabolic flow. Due to the repetitive nature of the geometry in the axial direction, the flow exhibits periodically repeating behavior after some initial development length. Calculations have been made for various values of the axial length parameter and two Prandtl numbers for two different fin geometries. Results indicate that in the periodic fully developed regime, for a Prandtl number of 0.7, a tube with staggered arrangement of fins produces less heat transfer enhancement than a tube with continuous fins. A tube with in-line arrangement of fins gives about as much heat transfer augmentation as the tubes with either continuous or staggered fins but with a much less pressure drop penalty. Local quantities such as the axial velocity profiles and the variation of centerline axial velocity give a good physical understanding of the governing phenomena.

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